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zvonat [6]
3 years ago
8

1.The two legs of a right triangle measures 3 feet and 2 feet. What is the length of the hypotenuse?

Mathematics
1 answer:
Dominik [7]3 years ago
4 0

Answer:

5; you add the two legs for the hypotenuse

Step-by-step explanation:

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can someone show me how to find the general solution of the differential equations? really need to know how to do it for the upc
mariarad [96]
The first equation is linear:

x\dfrac{\mathrm dy}{\mathrm dx}-y=x^2\sin x

Divide through by x^2 to get

\dfrac1x\dfrac{\mathrm dy}{\mathrm dx}-\dfrac1{x^2}y=\sin x

and notice that the left hand side can be consolidated as a derivative of a product. After doing so, you can integrate both sides and solve for y.

\dfrac{\mathrm d}{\mathrm dx}\left[\dfrac1xy\right]=\sin x
\implies\dfrac1xy=\displaystyle\int\sin x\,\mathrm dx=-\cos x+C
\implies y=-x\cos x+Cx

- - -

The second equation is also linear:

x^2y'+x(x+2)y=e^x

Multiply both sides by e^x to get

x^2e^xy'+x(x+2)e^xy=e^{2x}

and recall that (x^2e^x)'=2xe^x+x^2e^x=x(x+2)e^x, so we can write

(x^2e^xy)'=e^{2x}
\implies x^2e^xy=\displaystyle\int e^{2x}\,\mathrm dx=\frac12e^{2x}+C
\implies y=\dfrac{e^x}{2x^2}+\dfrac C{x^2e^x}

- - -

Yet another linear ODE:

\cos x\dfrac{\mathrm dy}{\mathrm dx}+\sin x\,y=1

Divide through by \cos^2x, giving

\dfrac1{\cos x}\dfrac{\mathrm dy}{\mathrm dx}+\dfrac{\sin x}{\cos^2x}y=\dfrac1{\cos^2x}
\sec x\dfrac{\mathrm dy}{\mathrm dx}+\sec x\tan x\,y=\sec^2x
\dfrac{\mathrm d}{\mathrm dx}[\sec x\,y]=\sec^2x
\implies\sec x\,y=\displaystyle\int\sec^2x\,\mathrm dx=\tan x+C
\implies y=\cos x\tan x+C\cos x
y=\sin x+C\cos x

- - -

In case the steps where we multiply or divide through by a certain factor weren't clear enough, those steps follow from the procedure for finding an integrating factor. We start with the linear equation

a(x)y'(x)+b(x)y(x)=c(x)

then rewrite it as

y'(x)=\dfrac{b(x)}{a(x)}y(x)=\dfrac{c(x)}{a(x)}\iff y'(x)+P(x)y(x)=Q(x)

The integrating factor is a function \mu(x) such that

\mu(x)y'(x)+\mu(x)P(x)y(x)=(\mu(x)y(x))'

which requires that

\mu(x)P(x)=\mu'(x)

This is a separable ODE, so solving for \mu we have

\mu(x)P(x)=\dfrac{\mathrm d\mu(x)}{\mathrm dx}\iff\dfrac{\mathrm d\mu(x)}{\mu(x)}=P(x)\,\mathrm dx
\implies\ln|\mu(x)|=\displaystyle\int P(x)\,\mathrm dx
\implies\mu(x)=\exp\left(\displaystyle\int P(x)\,\mathrm dx\right)

and so on.
6 0
4 years ago
A game that has a take of two cards with 10 red guards for two girls and two yellow cards are you randomly choose to go to find
Svetach [21]

Answer:

The probability of choosing two red cards would be 3/8

Step-by-step explanation:

The probability of choosing 1 red card is 10/16; the probability of choosing a second red card would then be 9/15.

P(2 red) = 10/16(9/15) = 90/240 = 3/8.

3 0
3 years ago
-3x > 24 on a number line
lianna [129]

\text {Hey! Here is the number line you requested}

\text {This equation will also equal...}

x

\text {How do you get that answer?} \text {Simple! You just divide both sides by 3}

-3x/3>24/-3

\text {Final Answer}

x

\text {Best of Luck!}

\text {-LimitedX}

4 0
3 years ago
HELP ASAP! I need the answer to all 3 of these questions.
Leokris [45]

Answer:

I think that number one is 26, two is -4, and three is -4

Step-by-step explanation:

To solve for number one replace 8 with (x) so 3(8) + 2. 3 x 8 = 24 and 24+2 = 26

Numbers 2 and 3 appear to be the same problem so just do 3(-2) + 2 (Because you replace the number with the x) 3(-2) = -6 + 2 = -4!

I hope that helped!

3 0
3 years ago
Each side of a square is increasing at a rate of 2 cm/s. at what rate is the area of the square increasing when the area of the
faltersainse [42]
Let x(t) =  the length of a side of the square (cm) at time t (s).
The rate of change of x is given as
\frac{dx}{dt} =2 \,  \frac{cm}{s}

The area (cm²) at time t is 
A = x²

The rate of change of the area with respect to time is
\frac{dA}{dt} = \frac{dA}{dx}  \frac{dx}{dt} =2 \frac{dA}{dx} =2(2x)=4x \,  \frac{cm^{2}}{s}

When A = 9 cm², then x = √9 = 3cm. Hence obtain
\frac{dA}{dt} = 4(3) = 12 \,  \frac{cm^{2}}{s}

Answer: 12 cm²/s

3 0
3 years ago
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